No abstract

We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

The aim of the present paper is to study Ricci soliton, η-Ricci soliton and various types of curvature tensors on Generalized Sasakian space form. We have also studied conformal Killing vector field, torse forming vector field on Generalized Sasakian space form. We have also established suitable examples of kenmotsu manifold, Sasakian manifold and cosymplectic manifold respectively. According to Perelman [8], we know that a Ricci soliton on a compact manifold is a gradient Ricci soliton.

This paper characterizes the warping functions for a multiply generalized Robertson–Walker space-time to get an Einstein space [Formula: see text] with a quarter-symmetric connection for different dimensions of [Formula: see text] (i.e. (1). dim [Formula: see text] (2). dim [Formula: see text]) when all the fibers are Ricci flat. Then we have also computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of [Formula: see text] (i.e. (1). dim [Formula: see text] (2). dim [Formula: see text] (3). dim [Formula: see text]) and all the fibers are Ricci flat. In the last section, we have given two examples of multiply generalized Robertson–Walker space-time with respect to quarter-symmetric connection.

No abstract